/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR u v x y z)
(RULES
++(.(x,y),z) -> .(x,++(y,z))
++(nil,y) -> y
if(false,x,y) -> x
if(true,x,y) -> x
merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
merge(nil,y) -> y
merge(x,nil) -> x
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 MERGE(.(x,y),.(u,v)) -> IF(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 MERGE(.(x,y),.(u,v)) -> MERGE(.(x,y),v)
 MERGE(.(x,y),.(u,v)) -> MERGE(y,.(u,v))
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
 MERGE(.(x,y),.(u,v)) -> IF(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 MERGE(.(x,y),.(u,v)) -> MERGE(.(x,y),v)
 MERGE(.(x,y),.(u,v)) -> MERGE(y,.(u,v))
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MERGE(.(x,y),.(u,v)) -> MERGE(.(x,y),v)
 MERGE(.(x,y),.(u,v)) -> MERGE(y,.(u,v))
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->->Cycle:
->->-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 MERGE(.(x,y),.(u,v)) -> MERGE(.(x,y),v)
 MERGE(.(x,y),.(u,v)) -> MERGE(y,.(u,v))
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->Projection:
 pi(MERGE) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 MERGE(.(x,y),.(u,v)) -> MERGE(.(x,y),v)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MERGE(.(x,y),.(u,v)) -> MERGE(.(x,y),v)
->->-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x

Problem 1.1: 

Subterm Processor:
-> Pairs:
 MERGE(.(x,y),.(u,v)) -> MERGE(.(x,y),v)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->Projection:
 pi(MERGE) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 ++#(.(x,y),z) -> ++#(y,z)
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->Projection:
 pi(++#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ++(.(x,y),z) -> .(x,++(y,z))
 ++(nil,y) -> y
 if(false,x,y) -> x
 if(true,x,y) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 merge(nil,y) -> y
 merge(x,nil) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.